# Mathematics

- Credits: 6
- Ending: Examination
- Range: 20sP
- Semester: winter
- Year: 2
- Faculty of Business Economics with seat in Košice

## Teachers

## Included in study programs

**Teaching results**

The aim of the course is to provide student with knowledge of linear algebra and mathematical analysis. The student will learn the theoretical foundations and principles of solving different types of problems from selected two areas of mathematics. After completing the course, he will be able to solve simpler and more complex tasks that he will encounter during his further study both on quantitatively oriented subjects and on other subjects with an economic focus.

Knowledge:

The student will master the theoretical foundations of linear algebra such as vector, linear combination of vectors, linear dependence and independence of vectors, he will be able to define a matrix, a rank of matrix, a determinant and an inverse matrix, to describe the principle of solving matrix equations and two basic methods of solving systems of linear equations namely Gaussian elimination method and Cramer's rule. The student will know to define the elementary functions and their properties, the limits and the continuity of the functions, the sequences and the limits of the sequences; he will master the basic definitions and statements concerning the differential calculus of one real variable as well as the basic definitions and statements of integral calculus.

Skills:

The student will be able to solve simpler and more complex problems in linear algebra and mathematical analysis. They will be able to work with vectors, verify the linear dependence and independence of vectors, to determine the rank of a matrix, to calculate a determinant, to find an inverse matrix, to solve matrix equations and systems of linear equations with three or more variables. The student will be able to determine domain and basic properties of a function, to calculate the limits of the sequence and the limits of various functions, the derivatives of the simple and complex functions, to determine the intervals of monotonicity, convexity and concavity of a function and sketch a graph of a function. The student will be able to compute indefinite and definite integral of a real function by decomposition, substitution and per partes and will be able to use the Newton-Leibnitz formula.

Competences:

After completing the course, the student will be able to solve simpler and more complex problems in linear algebra and mathematical analysis. The student will be ready to solve various assignments by their transformation into a mathematical problem. He will be able to apply their knowledge to real problems of a quantitative nature which he will encounter in his further study. The knowledge acquired in this course represent the basis for successful completion of courses of quantitative or economic nature.

**Indicative content**

Consultation:

Logic. Introduction to linear algebra: concept of vector, linear combination of vectors, linear dependence and independence of vectors. Concept of matrix and work with matrices, rank of matrix. Determinants, inverse matrices, matrix equations. Systems of linear equations, Gaussian elimination method, Cramer's rule. Function of one real variable. Function properties. Sequences. Arithmetic and geometric sequence. Sequence limit. Continuity and limit of a function. Differential calculus of a function of one variable. Monotonicity, convexity and concavity of a function. To draw the graph of the function. Introduction to integral calculus - indefinite integral. Integration by decomposition, per partes method and substitution method. Definite integral, Newton-Leibnitz formula.

Self-study:

Vector, linear combination of vectors, linear dependence and independence of vectors. Matrices and work with matrices, rank of matrices. Determinants, Sarrus's rule, inverse matrices, matrix equations. System of linear equations, Frobeni's theorem, Gaussian elimination method, Cramer's rule. Function of one real variable. Function properties. Even and odd function, periodicity of function, inverse function. Sequences. Arithmetic and geometric sequence. Sequence limit. Limit of a function. Differential calculus of a function of one variable. Monotonicity, convexity and concavity of a function. The course of the function. Preparation for the semester test. Introduction to integral calculus - indefinite integral. Integration by decomposition, per partes method and substitution method. Definite integral, Newton-Leibnitz formula.

**Support literature**

1. DVOŘÁKOVÁ, Ľ. 2020. Lineární algebra 2. CVUT Praha, 2020. ISBN: 978-8-001-06721-5

2. LUCKÁ, M. 2016. Úvod do matematickej analýzy. STU, 2016. ISBN: 978-8-022-74489-8

3. MEZNÍK, I. 2018. Základy matematiky pro ekonomii a management. Akademické nakladatelství CERM, 2018. ISBN: 978-8-021-45522-1

4. NAGY, J. – NAVRÁTIL, O. 2017. Matematická analýza. CVUT Praha, 2017. ISBN: 978-8-001-06142-8

5. PLETANOVÁ, E. – VONDRÁČKOVÁ, J. 2018. Matematická analýza. CVUT, 2018. ISBN: 978-8-001-06441-2

6. SAKÁLOVÁ, K. – SIMONKA, Z. – STREŠŇÁKOVÁ, A. Matematika: lineárna algebra. 2. vyd. Bratislava: Vydavateľstvo EKONÓM, 2015.

Supplementary literature:

7. ALESKEROV, F. – ERSEL, H. – PIONTKOVSKI, D. 2011. Linear Algebra for Economists. Springer, 2011. ISBN: 978-3-642-205699

8. BRANNAN, D. 2021. A first course in mathematical analysis. Cambridge University Press, 2021. ISBN: 978-0-521-68424-8

9. GORODENTSEV, A. L. 2016. Algebra I. Springer. 2016. ISBN: 978-3-319-45284-5

10. SYDSAETER, K. – HAMMOND, P. – STROM, A. – CARVAJAL, A. 2016. Essential Mathematics for Economics Analysis, 5th edition, Pearson, 2016, ISBN: 978-1-292-07461-0

**Syllabus**

Consultation: Logic. Introduction to linear algebra: concept of vector, linear combination of vectors, linear dependence and independence of vectors. Concept of matrix and work with matrices, rank of matrix. Determinants, inverse matrices, matrix equations. Systems of linear equations, Gaussian elimination method, Cramer's rule. Function of one real variable. Function properties. Sequences. Arithmetic and geometric sequence. Sequence limit. Continuity and limit of a function. Differential calculus of a function of one variable. Monotonicity, convexity and concavity of a function. To draw the graph of the function. Introduction to integral calculus - indefinite integral. Integration by decomposition, per partes method and substitution method. Definite integral, Newton-Leibnitz formula. Self-study: Vector, linear combination of vectors, linear dependence and independence of vectors. Matrices and work with matrices, rank of matrices. Determinants, Sarrus's rule, inverse matrices, matrix equations. System of linear equations, Frobeni's theorem, Gaussian elimination method, Cramer's rule. Function of one real variable. Function properties. Even and odd function, periodicity of function, inverse function. Sequences. Arithmetic and geometric sequence. Sequence limit. Limit of a function. Differential calculus of a function of one variable. Monotonicity, convexity and concavity of a function. The course of the function. Preparation for the semester test. Introduction to integral calculus - indefinite integral. Integration by decomposition, per partes method and substitution method. Definite integral, Newton-Leibnitz formula.

**Requirements to complete the course**

individual work, test

combined exam

• test - 40%

• combined exam - 60%

**Student workload**

• participation in consultation - 20 hours

• self-study - 32 hours

• preparation for consultation - 26 hours

• preparation for the semester test - 26 hours

• preparation for the exam - 52 hours

Total: 156 hours

**Language whose command is required to complete the course**

Slovak

Date of approval: 15.02.2023

Date of the latest change: 26.01.2022